CN105389839A - Fluid-analysis-based fluid parameter estimation method - Google Patents
Fluid-analysis-based fluid parameter estimation method Download PDFInfo
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Abstract
The invention provides a fluid-analysis-based fluid parameter estimation method. The method comprises the steps: carrying out empirical mode decomposition; to be specific, decomposing each frame of collected fluid velocity field into modes with different frequencies, thereby keeping information in a frequency domain; carrying out fluid velocity field dimensionality reduction; to be specific, carrying out integration on the decomposed model set and compressing the integrated one into a base and projecting calculation in three-dimensional space to sub space with a small scale, thereby reducing the calculation cost substantially; carrying out fluid simulation parameter estimation; to be specific, carrying out fluid simulation parameter back deduction in the sub space by using the collected fluid data according to an euler fluid simulation method; and carrying out re-simulation or fluid sequence editing; to be specific, reproducing a collected fluid sequence by using the fluid simulation parameter obtained by back deduction or carrying out parameter and boundary condition modification, and editing the fluid sequence. According to the invention, the empirical mode decomposition process is accelerated by using a GPU; and implementation of the process in the three-dimensional space is improved, so that the process can be completed within acceptable time.
Description
Technical field
The present invention relates to the technical field of fluid emulation, be specifically related to a kind of fluid parameter method of estimation based on fluid analysis.
Background technology
From the nineties initial stage, having there is a variety of fluid emulation technology in field of Computer Graphics, carries out discretize and iterative to incompressible Na Wei-Stokes.In recent years, a large amount of fluid acquisition technology has been there is, such as particle image velocimetry method (ParticleImageVelocimetry), time resolution schlieren system (Time-resolvedSchlierenSystem), flow surface modeling, method etc. based on optical flow analysis in computer graphics, Fluid Mechanics Computation and relevant engineering discipline.Due to nonlinear of the fluid, astable characteristic, existing analytical technology (as Fourier transform) is difficult to obtain desirable effect, and the fluid data therefore collected needs more powerful analysis means to describe the internal feature of their complexity.
The progress in current forward position is attempting to reduce the difference between fluid emulation with fluid acquisition, such as, extract with the video water surface that physical message guides, in conjunction with the improvement type optical flow algorithm etc. of fluid simulation process.Although these methods attempt to utilize fluid realistic model to improve the accuracy of image data, they can not restore a simulation sequence from the angle of model, and just make improvement in the aspect gathered.On the other hand, a lot of method can realize the control of shape in convection cell emulation, different fluid sequences can be createed as required, utilize the fluid that collects can regard as target a kind ofly can cross over emulation and collection difference feasible method to control fluid emulation, but this control can not reappear the detail content in fluid, and it is approximate to provide roughly in overall shape.
There is a large amount of three-dimensional datas in fluid application scenarios, the bottleneck that calculated amount is normally very large.A kind of well solution is combined with dimension reduction method by analysis means, utilizes sub-space technique to reduce computing cost.What traditional fluid dimensionality reduction technology utilized is the base that principal component analysis (PCA) (PCA) produces, it is minimum that the method for this structure base maintains error naturally, but the information on shortage frequency domain, the details of fluid can be lost, and the mutual interference of information on different frequency can be caused, need to improve to base the generation preventing these situations.
In order to solve the problem, the present invention proposes a kind of fluid parameter method of estimation based on fluid analysis of novelty, the method utilizes the information of more advanced analysis means convection cell different frequency to be described, combine to reduce calculated amount with dimension reduction method, by the optimization method of reverse estimating of fluid equation parameter, fluid simulation process is mutually integrated with the fluid data collected, in order to realize heavily emulating and the object such as editor.
Summary of the invention
The technical problem to be solved in the present invention is: provide a kind of fluid analysis means considering frequency information, and achieves the leap of emulation from fluid acquisition to fluid by the method optimized, and by the mode of dimensionality reduction, computation complexity of the present invention is reduced.
The technical solution used in the present invention is: a kind of fluid parameter method of estimation based on fluid analysis, comprises following four steps:
Step (1), empirical mode decomposition: each frame of fluid velocity field collected is carried out to the empirical mode decomposition on three dimensions, obtain velocity field mode on a different frequency;
Step (2), fluid velocity field dimensionality reduction: the mode set principal component of each frequency is analyzed, extract the proper vector that eigenwert is large, all frequency abstractions being gone out proper vector is collected in an overall set, base is formed through orthonormalization, each frame speed field is projected in the subspace of this group base formation, reach the object of dimensionality reduction;
Step (3), fluid simulation parameter are estimated: projected to by the incompressible Navier Stokes equation of unknown parameters in the subspace of the base composition obtained in step (2), according to each the frame speed field after dimensionality reduction, estimate the unknown parameter (viscosity and external force) in incompressible Navier Stokes equation;
The editor of step (4), heavily emulation or fluid sequence: use the parameter obtained in step (3), the heavily emulation of fluid can be carried out, the parameter obtained in modify steps (3) or by increasing border base, can carry out the editor of fluid.
Principle of the present invention is:
(1) suppose that existing fluid sequence meets Navier Stokes equation, and the unknown parameters in equation, by the method optimized, parameter estimation can be gone out, and the parameter estimated may be used for heavily emulating, and also may be used for the editor of fluid.
(2) choosing for base in fluid dimensionality reduction, traditional PCA base is beyond expression the information of frequency, thus selecting experience mode decomposition of the present invention, decomposite the mode of different frequency range adaptively, and carry out in each frequency range inside respectively when utilizing PCA to compress, again result is gathered and operative norm orthogonalization, ensure that each frequency range has the proper vector of candidate to be selected into the set of base, therefore can guarantee the information comprising all frequency ranges.
(3) for the empirical mode decomposition in three dimensions, traditional method is also inapplicable, mainly cannot carry out in three-dimensional for solving of envelope.The present invention uses thin plate spline matching coenvelope, lower envelope in three dimensions, empirical mode decomposition can be expanded in three-dimensional and carry out, and utilizes GPU to accelerate the execution of this process.
The present invention's being a little compared with prior art:
1, the parameter come with the method optimized in estimating of fluid equation of the present invention's proposition, make an existing fluid sequence can be reduced to a simulation process, and existing fluid sequence can only be reduced into its velocity field by existing method, and parameter in equation is still unknown.
2, existing fluid analysis method is contrasted, the subspace using empirical mode decomposition as base that the present invention proposes can describe the characteristic of fluid on different frequency better, comprise the overall and details under different scale, and when avoiding heavily emulation on different frequency range fluid energy mutually disturb.
3, existing method of carrying out empirical mode decomposition in three dimensional fluid mainly by three dimensions according to certain sequence of rules, become the one-dimensional space, again according to one-dimensional signal process, but the process of serializing can destroy original three-dimensional topology relation, make the result of empirical mode decomposition can produce the fluctuation of noise and mistake.The present invention proposes the thin plate spline function completely in three dimensions, and empirical mode decomposition can be made directly to perform in three dimensions, improves accuracy and the details performance of this process.
Accompanying drawing explanation
Fig. 1 is the fluid parameter method of estimation process flow diagram based on fluid analysis;
Fig. 2 is fluid velocity field empirical mode decomposition comparison diagram, and wherein Fig. 2 (a) is velocity field cross section, and Fig. 2 (b) is sequencing method result cross section, and Fig. 2 (c) is thin plate spline methods and results cross section;
Fig. 3 is the result in emulated data, wherein Fig. 3 (a) is known array schematic diagram, Fig. 3 (b) attaches most importance to simulation sequence schematic diagram, and Fig. 3 (c) is for editing 1 schematic diagram in border, and Fig. 3 (d) is for editing 2 schematic diagram in border;
Fig. 4 is the result in image data, and wherein Fig. 4 (a) is that known array increases viscosity schematic diagram, and Fig. 4 (b) simulation sequence of attaching most importance to increases external force schematic diagram;
Fig. 5 is the comparing of empirical mode decomposition base and PCA base in image data, wherein Fig. 5 (a) is known array schematic diagram, Fig. 5 (b) is for heavily to emulate schematic diagram with empirical mode decomposition base, and Fig. 5 (c) is for heavily to emulate schematic diagram with PCA base.
Embodiment
Fig. 1 gives the overall process flow of the fluid parameter method of estimation based on fluid analysis, further illustrates the present invention below in conjunction with other the drawings and the specific embodiments.
The invention provides a kind of fluid parameter method of estimation based on fluid analysis, key step is described below:
1, empirical mode decomposition
The effect of empirical mode decomposition input signal is decomposed into the intrinsic mode function and surplus that can describe signal characteristic on different scale by " screening " operation, and its process is as shown in algorithm 1.Coenvelope in this algorithm, lower envelope are obtained by Cubic Spline Functions Fitting maximum point, minimum point set." IMF stop condition " general accepted standard is adjacent h [k], and h [k-1] standard deviation is less than a threshold value.Each time in " screening " process, in signal margin, the information of higher frequency band is extracted as intrinsic mode function.This algorithm is widely used in the field such as signal transacting, image procossing, very effective for the scalar data be defined in the one-dimensional space.
The velocity field of fluid can be regarded as the phasor function be defined on three dimensions, and in the process of Conventional wisdom mode decomposition, the cubic spline function used due to the fit procedure of envelope can only be applied to the one-dimensional space, therefore needs the method using other to carry out matching envelope.Existing methodical solution is, according to certain rule, the burst on three dimensions is turned to one-dimensional signal, then processes.The method applied in the present invention utilizes the thin plate spline in three dimensions to carry out matching to be defined in data in three-dimensional, and each component of speed processes separately as a passage.The advantage of such process is that three-dimensional thin plate spline can keep the topological relation in three dimensions, therefore can obtain the decomposition result of level and smooth non-jitter.Three-dimensional spline-fitting can bring huge computation complexity, and the present invention utilizes GPU concurrent technique to accelerate, and computing time is significantly shortened.
In order to better coordinate subsequent treatment of the present invention, empirical mode decomposition requires further improvement: ensure that the result that each " screening " goes out is all passive field, and meet the boundary condition of raw data, the base that subsequent treatment is formed can produce passive and meet the sequence of boundary condition under any linear combination, need not carry out explicit constraint again.In addition, be forced to be decided to be twice to the screening number of times of each frame speed field data, namely the decomposition result of each frame comprises three frequency components (two intrinsic mode functions and a surplus).Empirical mode decomposition process after improvement is as shown in algorithm 2.Empirical mode decomposition of the present invention and existing sequencing method contrast as shown in Figure 2, can find out, the method for thin plate spline can produce smoothly, the result of non-jitter, and sequencing method lacks topology information, and noise is a lot.
2, fluid velocity field dimensionality reduction
Empirical mode decomposition is carried out to each frame of known fluid sequence, obtains the set of three frequency components.In each set, perform principal component analysis (PCA), select some proper vectors that eigenwert is maximum, combine and form new set, to this set operative norm orthogonalization, form the base B that dimensionality reduction is used.
B is one group of orthonormal basis, the mode that its composition filters out from three kinds of different frequency ranges.If B is the base of m dimension, the velocity field u of any frame can be regarded as n and ties up higher order vector, and u is projected as r under B, then there is u=Br and r ≈ B
tu (getting equal sign when u is positioned at the subspace of B generation).
Ordinary differential equation
can project in the subspace of B generation
linear differential equation
can project in the subspace of B generation
in like manner incompressible Navier Stokes equation
Also can project in the subspace of B generation.
3, fluid simulation parameter is estimated
The object that fluid parameter is estimated estimates unknown parameter in flow equation to use them to reappear fluid sequence in simulations.Because three dimensional fluid googol can produce a large amount of calculating according to amount, this step is carried out in the subspace of dimensionality reduction.
Each frame of known fluid sequence is all projected in the subspace of B generation, and the Navier Stokes equation of band unknown parameter is also projected in the subspace of B generation, and unknown parameter comprises viscosity ν and external force term f.Navier Stokes equation projects in subspace
wherein
for convection current matrix,
for stickiness matrix, the restriction of pressure item, divergence and boundary condition no longer appear in subspace, because just ensure that the velocity field that any linear combination produces all meets passive and boundary condition when constructing base B.
two matrixes can precomputation to accelerate.
The effect that stickiness and external force produce is not easy to distinguish, and acting in whole fluid sequence that the present invention supposes that external force term produces is little as far as possible, namely minimizes following objective function
this optimizing process is calculate maximum viscosity in essence, is required result in most instances.After viscosity ν tries to achieve, can substitute into
by the external force term of each frame
obtain.
4, heavily emulation or the editor of fluid sequence
By the fluid parameter that above-mentioned steps estimates, as known substitution Navier Stokes equation in heavy simulation process, the simulation sequence the same with known fluid sequence can be produced.Owing to obtaining the parameter used by emulation, can modify to parameter, border, accomplish real fluid sequence editor on physical layer.With emulated data be input experiment as shown in Figure 3, with image data be input experiment as shown in Figure 4.The experiment of contrast empirical mode decomposition Based PC A base as shown in Figure 5, PCA base is owing to there being the mixing of energy between different frequency, therefore the increase of the energy of high frequency increases the energy of low frequency mistakenly, and empirical mode decomposition base then can distinguish the energy of different frequency more accurately.
The technology contents that the present invention does not elaborate belongs to the known technology of those skilled in the art.
Although be described the illustrative embodiment of the present invention above; so that the technician of this technology neck understands the present invention; but should be clear; the invention is not restricted to the scope of embodiment; to those skilled in the art; as long as various change to limit and in the spirit and scope of the present invention determined, these changes are apparent, and all innovation and creation utilizing the present invention to conceive are all at the row of protection in appended claim.
Claims (4)
1. based on a fluid parameter method of estimation for fluid analysis, it is characterized in that: comprise following four steps:
Step (1), empirical mode decomposition: each frame of fluid velocity field collected is carried out to the empirical mode decomposition on three dimensions, obtain velocity field mode on a different frequency;
Step (2), fluid velocity field dimensionality reduction: the mode set principal component of each frequency is analyzed, extract the proper vector that eigenwert is large, all frequency abstractions being gone out proper vector is collected in an overall set, base is formed through orthonormalization, each frame speed field is projected in the subspace of this group base formation, reach the object of dimensionality reduction;
Step (3), fluid simulation parameter are estimated: projected to by the incompressible Navier Stokes equation of unknown parameters in the subspace of the base composition obtained in step (2), according to each the frame speed field after dimensionality reduction, estimate the unknown parameter in incompressible Navier Stokes equation, wherein this unknown parameter is viscosity and external force;
The editor of step (4), heavily emulation or fluid sequence: use the parameter obtained in step (3), the heavily emulation of fluid can be carried out, the parameter obtained in modify steps (3) or by increasing border base, can carry out the editor of fluid.
2. the fluid parameter method of estimation based on fluid analysis according to claim 1, it is characterized in that: the empirical mode decomposition in described step (1) is different from traditional empirical mode decomposition, need to realize on three dimensions, thin plate spline function is utilized to come matching coenvelope, lower envelope, and in decomposable process, keep the boundary shape of each mode to keep and input data consistent, and ensure as passive field, the base formed like this can ensure that its subspace need not rely on other to retrain just to meet boundary condition and the passive restriction of velocity field.
3. the fluid parameter method of estimation based on fluid analysis according to claim 1, it is characterized in that: the dimensionality reduction described in the dimensionality reduction of fluid velocity field in described step (2) is using the result of convection cell velocity field empirical mode decomposition as base, described dimensionality reduction is that the velocity field dimensionality reduction of core is different with svd from traditional, the method can keep the information on velocity field frequency domain, and the fluid details of high frequency also can be kept when radix amount is very few.
4. the fluid parameter method of estimation based on fluid analysis according to claim 1, it is characterized in that: the described parameter estimation that the fluid simulation parameter in described step (3) is estimated utilizes the incompressible Navier Stokes equation of unknown parameters, each the frame fluid velocity field collected is substituted into wherein, first utilize the means of optimization to try to achieve the optimal estimation of the viscosity in whole fluid time series, and then substitute into the estimation that equation obtains the external force of each frame.
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| CN110909472A (en) * | 2019-11-27 | 2020-03-24 | 北京航空航天大学 | Powder material simulation method based on mixed model |
| CN111241728A (en) * | 2020-01-03 | 2020-06-05 | 电子科技大学 | Intermittent Galerkin finite element numerical solution method of Euler equation |
| CN111990992A (en) * | 2020-09-03 | 2020-11-27 | 山东中科先进技术研究院有限公司 | Electroencephalogram-based autonomous movement intention identification method and system |
| CN113158531A (en) * | 2021-02-07 | 2021-07-23 | 南开大学 | Single-component and multi-component incompressible fluid simulation method utilizing deformation gradient |
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